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Implementation in partial equilibrium. (English) Zbl 1400.91165
Summary: Consider a society with a finite number of sectors (social issues or commodities). In a partial equilibrium (PE) mechanism a sector authority (SA) aims to elicit agents’ preference rankings for outcomes at hand, presuming separability of preferences, while such presumption is false in general and such isolated rankings might be artifacts. This paper studies what can be Nash implemented if we take such misspecification of PE analysis as a given institutional constraint. The objective is to uncover the kinds of complementarity across sectors that this institutional constraint is able to accommodate. Thus, in our implementation model there are several SAs, agents are constrained to submit their rankings to each SA separately and, moreover, SAs cannot communicate with each other. When a social choice rule (SCR) can be Nash implemented by a product set of PE mechanisms, we say that it can be Nash implemented in PE. We identify necessary conditions for SCRs to be Nash implemented in PE and show that they are also sufficient under a domain condition which identifies the kinds of admissible complementarities. Thus, the Nash implementation in PE of SCRs is examined in auction and matching environments.

91B14 Social choice
91B32 Resource and cost allocation (including fair division, apportionment, etc.)
Full Text: DOI
[1] Avery, C.; Hendershott, T., Bundling and optimal auctions of multiple products, Rev. Econ. Stud., 67, 3, 483-497, (2000) · Zbl 1055.91521
[2] Barberà, S.; Sonnenschein, H.; Zhou, L., Voting by committees, Econometrica, 59, 595-609, (1991) · Zbl 0734.90006
[3] Clarke, E. H., Multipart pricing of public goods, Public Choice, 11, 17-33, (1971)
[4] Dutta, B.; Sen, A., A necessary and sufficient condition for two-person Nash implementation, Rev. Econ. Stud., 58, 121-128, (1991) · Zbl 0717.90005
[5] Groves, T., Incentives in teams, Econometrica, 41, 617-631, (1973) · Zbl 0311.90002
[6] Hayashi, T., Smallness of a commodity and partial equilibrium analysis, J. Econ. Theory, 48, 279-305, (2013) · Zbl 1282.91186
[7] Hayashi, T.; Lombardi, M., Implementation in partial equilibrium, (2016), Available at SSRN
[8] Jackson, M. O., A crash course in implementation theory, Soc. Choice Welf., 18, 655-708, (2001) · Zbl 1069.91557
[9] Le Breton, M.; Sen, A., Separable preferences, strategyproofness and decomposability, Econometrica, 67, 605-628, (1999) · Zbl 1022.91020
[10] Lombardi, M.; Yoshihara, N., A full characterization of Nash implementation with strategy space reduction, Econ. Theory, 54, 131-151, (2013) · Zbl 1284.91023
[11] Maskin, E., Nash equilibrium and welfare optimality, Rev. Econ. Stud., 66, 23-38, (1999) · Zbl 0956.91034
[12] Maskin, E.; Sjöström, T., Implementation theory, (Arrow, K.; Sen, A. K.; Suzumura, K., Handbook of Social Choice and Welfare, (2002), Elsevier Science Amsterdam), 2002. pp. 237-288
[13] Moore, J.; Repullo, R., Nash implementation: a full characterization, Econometrica, 58, 1083-1100, (1990) · Zbl 0731.90009
[14] Repullo, R., A simple proof of Maskin’s theorem on Nash implementation, Soc. Choice Welf., 4, 39-41, (1987) · Zbl 0618.90007
[15] Shapley, L.; Scarf, H., On core and indivisibility, J. Math. Econ., 23-37, (1974) · Zbl 0281.90014
[16] Sjöström, T., On the necessary and sufficient conditions for Nash implementation, Soc. Choice Welf., 8, 333-340, (1991) · Zbl 0734.90007
[17] Vickrey, W., Counterspeculation, auctions, competitive sealed tenders, J. Finance, 16, 8-37, (1961)
[18] Vives, X., Small income effects: a Marshallian theory of consumer surplus and downward sloping demand, Rev. Econ. Stud., 54, 87-103, (1987) · Zbl 0695.90005
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